Using the transient hot-wire method, the thermal conductivity properties of the molten Li2O-B2O3 and K2O-B2O3 systems were measured. The thermal conductivity increases with decreasing the temperature due to the borate structure change. In addition, calculations of the one-dimensional Debye temperature and the phonon mean free paths as a function of temperature of the alkali borate systems were made. At a fixed temperature of 1273 K, the effect of the alkali oxide concentration on the thermal conductivity was evaluated. Within a range of 10-30 mol% Li2O (or K2O), a positive relationship between the thermal conductivity and 4-coordinate boron was obtained. However, below 10 mol% Li2O (or K2O), the change in the intermediate-range order of the borate structure had a more dominant effect on the thermal conductivity. Finally, the effect of cations on the thermal conductivity in the various molten R2O-B2O3 (R=Li, Na and K) systems was considered. Depending on the type of cation, the change in the ionization potential had an effect on the thermal conductivity and also resulted in a change in the bond strength.